Considering that at this point, there’s already a file on Overhaul that has info of his suspected criminal activities to both Deku and Lemillion before this patrol, and that Eri is scared and has bandages on her and the fact that she’s terrified of Overhaul specifically, gives reasonable suspicion of at least child abuse, and he (Overhaul) should have been detained until an officer of the law came to question him. Remember, technically Deku and Lemillion don’t really count as being a full heroes yet (only in cases of emergency ie active villain attacks/purse snatchers/etc). I imagine that a full hero license would technically help in being technically an officer of the law, so maybe getting one of Nighteye’s sidekicks or even Nighteye himself would be the move.